English

Quantum inequality in spacetimes with small curvature

General Relativity and Quantum Cosmology 2015-05-13 v2 Mathematical Physics math.MP Quantum Physics

Abstract

Quantum inequalities bound the extent to which weighted time averages of the renormalized energy density of a quantum field can be negative. They have mostly been proved in flat spacetime, but we need curved-spacetime inequalities to disprove the existence of exotic phenomena, such as closed timelike curves. In this work we derive such an inequality for a minimally-coupled scalar field on a geodesic in a spacetime with small curvature, working to first order in the Ricci tensor and its derivatives. Since only the Ricci tensor enters, there are no first-order corrections to the flat-space quantum inequalities on paths which do not encounter any matter or energy.

Keywords

Cite

@article{arxiv.1410.0665,
  title  = {Quantum inequality in spacetimes with small curvature},
  author = {Eleni-Alexandra Kontou and Ken D. Olum},
  journal= {arXiv preprint arXiv:1410.0665},
  year   = {2015}
}

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21 pages